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Circuit y(t)=|x(t)|, LIT system?

  1. Mar 31, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider a circuit which output is the absolute value of the input signal, this is, y(t)=|x(t)|?

    a) this circuit is not a LIT system because it implements a non linear operation;

    b) this circuit is a LIT system that creates phase distortion;

    c) this circuit is a LIT system that creates amplitude distortion;

    d) this circuit is a LIT system that creates amplitude and phase distortion.

    2. Relevant equations
    --

    3. The attempt at a solution
    My first thought was... it's not linear because it will "convert" only the negative part of the sinusoid but then... isn't this because of the phase? I can't decide between a) and b).

    Could someone please give a help?
     
  2. jcsd
  3. Mar 31, 2015 #2

    Stephen Tashi

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    Science Advisor

    To answer a mathematical question, you should think in terms of mathematics. What's the mathematical definition of a linear time independent system (- if that's what "LIT" abbreviates. The more common abbreviation is "LTI".)
     
  4. Mar 31, 2015 #3
    it means that the system will do the same no matter what time...
     
  5. Mar 31, 2015 #4

    Stephen Tashi

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    That isn't a mathematical description. Look up the mathematical definition of an LTI system. What mathematical laws must it follow?
     
  6. Mar 31, 2015 #5

    donpacino

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    Gold Member

    I think you mean LTI: Linear Time invariant.
    for a system to be LTI it has to meet to criteria.
    1. it has to be linear
    (S is a system operator)

    S [ x1(t) + x2(t)] = S [x1(t)] + S [x2(t)]

    and

    S [ a x1(t) ] = a S [x1(t) ]

    2. it has to be time invariant
    y(t - T) = S [x(t - T)]
    for any T or t

    so znaya, does your function meet the first criteria?
    use two inputs, say -2 and 2
     
  7. Mar 31, 2015 #6
    http://www.icoachmath.com/math_dictionary/Linear_Function.html

    Definition of Linear Function
    A function that can be graphically represented in the Cartesian coordinate plane by a straight line is called a Linear Function.
     
  8. Mar 31, 2015 #7
    for x=-2, y=2
    for x=2, y=2
    for x=(2+(-2)) y=0

    i see...

    so it seems my first thought was right...
     
  9. Mar 31, 2015 #8
    Stephen Tashi, donpacino, thank you so much for your help.
     
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